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The X0(2900) and its heavy quark spin partners in molecular picture
Mei-Wei Hu, Xue-Yi Lao, Pan Ling, Qian Wang
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The \begin{document}$X_0(2900)$\end{document} observed by the LHCb Collaboration recently in the \begin{document}$D^-K^+$\end{document} invariant mass of the \begin{document}$B^+\to D^+D^-K^+$\end{document} process is the first exotic candidate with four different flavors, which opens a new era for the hadron community. Under the assumption that the \begin{document}$X_0(2900)$\end{document} is a \begin{document}$I(J^P)=0(0^+)$\end{document} \begin{document}$\bar{D}^*K^*$\end{document} hadronic molecule, we extract the whole heavy-quark symmetry multiplet formed by the \begin{document}$\left(\bar{D},\bar{D}^*\right)$\end{document} doublet and the \begin{document}$K^*$\end{document} meson. For the bound state case, there would be two additional \begin{document}$I(J^P)=0(1^+)$\end{document} hadronic molecules associated with the \begin{document}$\bar{D}K^*$\end{document} and \begin{document}$\bar{D}^*K^*$\end{document} channels as well as one additional \begin{document}$I(J^P)=0(2^+)$\end{document} \begin{document}$\bar{D}^*K^*$\end{document} molecule. In the light quark limit, they are \begin{document}$36.66~{\rm{MeV}}$\end{document} and \begin{document}$34.22~{\rm{MeV}}$\end{document} below the \begin{document}$\bar{D}K^*$\end{document} and \begin{document}$\bar{D}^*K^*$\end{document} thresholds, respectively, which are unambiguously fixed by the mass position of the \begin{document}$X_0(2900)$\end{document}. For the virtual state case, there would be one additional \begin{document}$I(J^P)=0(1^+)$\end{document} hadronic molecule strongly coupling to the \begin{document}$\bar{D}K^*$\end{document} channel and one additional \begin{document}$I(J^P)=0(2^+)$\end{document} \begin{document}$\bar{D}^*K^*$\end{document} molecule. Searching for these heavy quark spin partners will help shed light on the nature of the \begin{document}$X_0(2900)$\end{document}.
Study of BESIII Trigger Efficiencies with the 2018 J/ψ Data
M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, M. L. Chen, S. J. Chen, X. R. Chen, Y. B. Chen, Z. J Chen, W. S. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, S. X. Du, Y. L. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, M. Fritsch, C. D. Fu, Y. Gao, Y. G. Gao, I. Garzia, P. T. Ge, C. Geng, E. M. Gersabeck, A Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, S. Gu, Y. T. Gu, C.
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Using a dedicated data sample taken in 2018 on the J/ψ peak, we perform a detailed study of the trigger efficiencies of the BESIII detector. The efficiencies are determined from three representative physics processes, namely Bhabha-scattering, dimuon production and generic hadronic events with charged particles. The combined efficiency of all active triggers approaches 100% in most cases with uncertainties small enough as not to affect most physics analyses.
Joule-Thomson Expansion of Born-Infeld AdS Black Holes
Shihao Bi, Minghao Du, Jun Tao, Feiyu Yao
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In this paper, the Joule-Thomson expansion of Born-Infeld AdS black holes is studied in the extended phase space, where the cosmological constant is identified with the pressure. The Joule-Thomson coefficient, the inversion curves and the isenthalpic curves are discussed in detail by 4-dimensional black hole. The critical point of Born-Infeld black hole is depicted with varying parameter \begin{document}$ \beta $\end{document} and the charge Q. In \begin{document}$ T-P $\end{document} plane, the inversion temperature curves and isenthalpic curves are obtained with different parameter \begin{document}$ \beta $\end{document} and the charge Q. We find that the missing negative slope is still conserved in Born-Infeld black holes. We also extend our discussion to arbitrary dimension higher than 4. The critical temperature and the minimum of inversion temperature are compared, and the ratio is asymptotically \begin{document}$ 1/2 $\end{document} as Q increases or \begin{document}$ \beta\to\infty $\end{document} in \begin{document}$ D = 4 $\end{document} , and reproduce the previous results in higher dimension.
Thermodynamic extremality relations in the massive gravity
Deyou Chen, Jun Tao, Peng Wang
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A universal relation between the leading correction to the entropy and extremality was gotten in the work of Goon and Penco. In this paper, we extend this work to the massive gravity and investigate thermodynamic extremality relations in a topologically higher-dimensional black hole. A rescaled cosmological constant is added to the action of the massive gravity as a perturbative correction. This correction modifies the extremality bound of the black hole and leads to the shifts of the mass, entropy, etc. Regarding the cosmological constant as a variable related to pressure, we get the thermodynamic extremality relations between the mass and entropy, pressure, charge, parameters ci by accurate calculations, respectively. Finally, these relations are verified by a triple product identity, which shows that the universal relation exists in black holes.
Analysis of Bcτντ at CEPC
Taifan Zheng, Ji Xu, Lu Cao, Dan Yu, Wei Wang, Soeren Prell, Yeuk-Kwan E. Cheung, Manqi Ruan
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The precise determination of the \begin{document}$B_c \to \tau\nu_\tau$\end{document} branching ratio provides an advantageous opportunity for understanding the electroweak structure of the Standard Model, measuring the CKM matrix element \begin{document}$|V_{cb}|$\end{document} and probing new physics models. In this paper, we discuss the potential of measuring the processes of \begin{document}$B_c \to \tau\nu_\tau$\end{document} with \begin{document}$\tau$\end{document} decaying leptonically at the proposed Circular Electron Positron Collider (CEPC). We conclude that during the Z pole operation, the channel signal can achieve five \begin{document}$\sigma$\end{document} significance with \begin{document}$\sim 10^9$\end{document} Z decays, and the signal strength accuracies for \begin{document}$B_c \to \tau\nu_\tau$\end{document} can reach around 1% level at the nominal CEPC Z pole statistics of one trillion Z decays assuming the total \begin{document}$B_c \to \tau \nu_\tau$\end{document} yield is \begin{document}$3.6 \times 10^6$\end{document}. Our theoretical analysis indicates the accuracy could provide a strong constraint on the general effective Hamiltonian for the \begin{document}$b \to c\tau\nu$\end{document} transition. If the total \begin{document}$B_c$\end{document} yield can be determined to \begin{document}${\cal{O}}$\end{document}(1%) level of accuracy in the future, these results also imply \begin{document}$|V_{cb}|$\end{document} could be measured up to \begin{document}${\cal{O}}$\end{document}(1%) level of accuracy.
Effective Field Theory approach to lepto-philic self conjugate dark matter
Hrishabh Bharadwaj, Ashok Goyal
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We study the self conjugate dark matter (DM) particles interacting primarily with the standard model leptons in an effective field theoretical frame work. We consider SM gauge invariant effective contact interactions between the Majorana fermion, real scalar and a real vector DM with leptons by evaluating the Wilson coefficients appropriate for interaction terms upto dimension-8 and obtain constraints on the parameters of the theory from the observed relic density, indirect detection observations and from the DM-electron scattering cross-sections in the direct detection experiments. Low energy LEP data has been used to study sensitivity in the pair production of such low mass \begin{document}$ \leqslant$\end{document} 80 GeV DM particles. Pair production of DM particles of mass \begin{document}$\geqslant$\end{document} 50 GeV in association with mono-photons at the proposed ILC has rich potential to probe such effective operators.
Probing the universality of acceleration scale in the modified Newtonian dynamics with SPARC galaxies
Xin Li, Su-Ping Zhao, Hai-Nan Lin, Yong Zhou
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We probe the universality of acceleration scale \begin{document}$ a_0$\end{document} in Milgrom's modified Newtonian dynamics (MOND) using the recently released rotation curve data from SPARC galaxies. We divide the SPARC data into difference subsamples according to the morphological types of galaxies, and fit the rotation curve data of each subsample with the theoretical prediction of MOND. MOND involves an arbitrary interpolation function which connects the Newtonian region and MOND region. Here we consider five different interpolation functions that are widely discussed in literatures. It is shown that the best-fitting \begin{document}$ a_0$\end{document} significantly depends on the interpolation functions. For a specific interpolation function, \begin{document}$ a_0$\end{document} also depends on the morphological types of galaxies, implying that \begin{document}$ a_0$\end{document} may be not a universal constant. Introducing a dipole correction on \begin{document}$ a_0$\end{document} can significantly improves the fits, and the dipole directions for four in five interpolation functions point towards an approximately consistent direction, but \begin{document}$ a_0$\end{document} still varies for differently interpolation functions.
Minimal Length Effects on Motion of a Particle in Rindler Space
Xiaobo Guo, Kangkai Liang, Benrong Mu, Peng Wang, Mingtao Yang
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Various quantum theories of gravity predict the existence of a minimal measurable length. In this paper, we study effects of the minimal length on the motion of a particle in the Rindler space under a harmonic potential. This toy model captures key features of particle dynamics near a black hole horizon, and allows us to make three observations. First, we find that the chaotic behavior is stronger with the increases of the minimal length effects, which manifests that the maximum Lyapunov characteristic exponents mostly grow, and the KAM curves on Poincaré surfaces of section tend to disintegrate into chaotic layers. Second, in the presence of the minimal length effects, it can take a finite amount of Rindler time for a particle to cross the Rindler horizon, which implies a shorter scrambling time of black holes. Finally, it shows that some Lyapunov characteristic exponents can be greater than the surface gravity of the horizon, violating the recently conjectured universal upper bound. In short, our results reveal that quantum gravity effects may make black holes prone to more chaos and faster scrambling.
Inclusive $ {{\Upsilon(1S,2S,3S)}}$ photoproduction at the CEPC
Xi-Jie Zhan, Jian-Xiong Wang
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The inclusive \begin{document}$ \Upsilon(1S,2S,3S) $\end{document} photoproduction at the future Circular-Electron-Positron-Collider (CEPC) is studied based on the non-relativistic QCD (NRQCD) factorization formalism. Including the contributions from both direct and resolved photons, we present different distributions for \begin{document}$ \Upsilon(1S,2S,3S) $\end{document} production and the results show there will be considerable events, which means that a well measurements on the \begin{document}$ \Upsilon $\end{document} photoprodution could be performed to further study on the heavy quarkonium physics at electron-positron collider in addition to hadron colliders. This supplement study is very important to clarify the current situation of the heavy quarkonium production mechanism.
Slowly rotating Einstein-bumblebee black hole solution and its greybody factor in a Lorentz violation model
Chikun Ding, Xiongwen Chen
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We obtain an exact slowly rotating Einstein-bumblebee black hole solution by solving the corresponding \begin{document}$rr$\end{document} and \begin{document}$t\phi$\end{document} components of the gravitational field equations in both cases: A, \begin{document}$b_\mu=(0,b(r),0,0)$\end{document}; B, \begin{document}$b_\mu= (0,b(r), \mathfrak{b}(\theta),0)$\end{document}. Then we check the other gravitational field equations and the bumblebee field motion equations by using this solution. We find that in the case A, there exists a slowly rotating black hole solution indeed for arbitrary LV (Lorentz violation) coupling constant \begin{document}$\ell$\end{document}; however as in the case B, there exists this slowly rotating solution if and only if the coupling constant \begin{document}$\ell$\end{document} is as small as or smaller than the angular momentum a. Till now there seems to be no full rotating black hole solution, so one can't use the Newman-Janis algorithm to generate a rotating solution in Einstein-bumblebee theory. It is similar as that in Einstein-aether theory where there exists only some slowly rotating black hole solutions. In order to study the effects of this Lorentz symmetry broken, we consider the black hole greybody factor and find that when angular index \begin{document}$l=0$\end{document}, the LV constant \begin{document}$\ell$\end{document} decreases the effective potential and enhances the absorption probability, which is similar to that of the non-minimal derivative coupling theory.
Four α correlations in nuclear fragmentation: a game of resonances
M. Huang, A. Bonasera, S. Zhang, H. Zheng, D. X. Wang, J. C. Wang, N. Song, X. Tang, L. Lu, G. Zhang, Z. Kohley, M. R. D. Rodrigues, Y. G. Ma, S. J. Yennello
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Heavy ion collisions near the Fermi energy produce a ‘freezout’ region where fragments appear and later decay emitting mainly neutrons, protons, alphas and gamma rays. These products carry information on the decaying nuclei in the medium. Fragmentation events might result in high yields of boson particles, especially alpha particles, and carry important information on the nuclear Bose Einstein Condensate (BEC). We study ‘in medium’ 4α correlations and link them to the ‘fission’ of 16O in two 8Be in the ground state or 12C*(Hoyle State)+α. Using novel techniques for the correlation functions we confirm a resonance of 16O at 15.2 MeV excitation energy and the possibility of a lower resonance close to 14.72 MeV. The latter resonance is the result of all α particles having 92 keV relative kinetic energies.
New look at Geiger-Nuttall Law and α clustering of heavy nuclei
Yi-Bin Qian, Zhong-Zhou Ren
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The Geiger-Nuttall (GN) law of α decay is commonly explained in terms of the quantum tunneling phenomenon. In this study, we show that such an explanation is actually not enough regarding the α particle clustering. Such an inference is drawn from the exploration on the involved coefficients of the GN law based on the conventional recognition of α decay, namely the formation of α cluster and its subsequential penetration. The specific roles of the two former processes, played in the GN law, are manifested themselves via the systematical analysis of the calculated and experimental α decay half-lives versus the decay energies across the Z=82 and N=126 shell closures. The α-cluster preformation probability is then found to behave as a GN-like pattern. This previously ignored point is explicitly demonstrated as the product of the interplay between the mean-field and pairing effect, which in turn reveals the structural influence on the formation of α cluster in a simple and clear way. Besides providing an effective way to evaluate the amount of surface α clustering in heavy nuclei, the present conjecture supports other theoretical treatments of the α preformation probability.
Impact of LHCb 13 TeV W and Z pseudo-data on the Parton Distribution Functions
Qilin Deng, Qundong Han, Hang Yin, Sayipjamal Dulat, Tie-Jiun Hou, C.–P. Yuan
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We studied the potential of the LHCb 13 TeV single W± and Z boson pseudo-data on constraining the Parton Distribution Functions (PDFs) of the proton. As an example, we demonstrated the sensitivity of the LHCb 13 TeV data, collected with an integrated luminosity of 5 \begin{document}$ {\rm{fb}}^{-1}$\end{document} and 300 \begin{document}$ {\rm{fb}}^{-1}$\end{document} , respectively, to reducing the PDF uncertainty bands of the CT14HERA2 PDFs, using the error PDF updating package EPUMP. For that, the sensitivities of various experimental observables have been compared. Generally, sizable reductions in PDF uncertainties can be observed in the 300 \begin{document}$ {\rm{fb}}^{-1}$\end{document} data sample, particularly in the small x region. The double differential cross section measurement on Z boson pT and rapidity can greatly reduce the uncertainty bands of u and d quarks in almost all x range, as compared to various single observable measurements.
Shell corrections with finite temperature covariant density functional theory
W. Zhang, W.-L. Lv, T.-T. Sun
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The temperature dependence of the shell corrections to the energy \begin{document}$\delta E_{\rm{shell}}$\end{document}, entropy \begin{document}$T \delta S_{\rm{shell}}$\end{document}, and free energy \begin{document}$\delta F_{\rm{shell}}$\end{document} are studied employing the covariant density functional theory for closed-shell nuclei. Taking \begin{document}$^{144}$\end{document}Sm as an example, studies show that unlike the widely-used exponential dependence \begin{document}$\exp(-E^*/E_d)$\end{document}, the \begin{document}$\delta E_{\rm{shell}}$\end{document} exhibits non-monotonous behavior, i.e., first drops 20% approaching temperature \begin{document}$0.8$\end{document} MeV, and then fades away exponentially. Both the shell corrections to the free energy \begin{document}$\delta F_{\rm{shell}}$\end{document} and to the entropy \begin{document}$T \delta S_{\rm{shell}}$\end{document} can be approximated well using the Bohr-Mottelson forms \begin{document}$\tau/\sinh(\tau)$\end{document} and \begin{document}$[\tau \coth(\tau)-1]/\sinh(\tau)$\end{document} respectively where \begin{document}$\tau\propto T$\end{document}. Further studies for shell corrections in other closed-shell nuclei \begin{document}$^{100}$\end{document}Sn and \begin{document}$^{208}$\end{document}Pb are performed and the same temperature dependencies are obtained.
Measurement of neutron energy spectra of 9Be(d,n)10B reaction with a thick beryllium target
Shuang-Jiao Zhang, Zhi-Jie Hu, Zhi-Ming Hu, Chao Han, Xiao-Hou Bai, Chang-Qi Liu, Chang Huang, Qin Xie, Dong-Ying Huo, Kang Wu, Yang-Bo Nie, Yan-Yan Ding, Kai Zhang, Yu Zhang, Zhi-Yong Deng, Rui Guo, Zheng Wei, Ze-En Yao
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The new measurements of the neutron energy spectra of the 9Be(d,n)10B reaction with a thick beryllium target are carried out by the fast neutron time-of-flight (TOF) spectrometer for the neutron emission angles \begin{document}$\theta=0^\circ$\end{document} and \begin{document}$45^\circ$\end{document}, and the incident deuteron energies are 250 keV and 300 keV, respectively. The neutron contributions from the 9Be(d,n)10B reaction are distributed relatively independently for the ground state of 10B, 1st, 2nd, and 3rd excited state of 10B. The branching ratio of the 9Be(d,n)10B reaction for different excited states of 10B are obtained for the neutron emission angles \begin{document}$\theta=0^\circ$\end{document} and \begin{document}$45^\circ$\end{document}, and the incident deuteron energies are 250 keV and 300 keV, respectively. The branching ratio of the 9Be(d,n)10B reaction for the 3rd excited state is decreasing with increasing of the incident deuteron energy, and the branching ratio for the ground state and 2nd excited state are rising with increasing of the neutron emission angles.
Instability of the regularized 4D charged Einstein-Gauss-Bonnet de-Sitter black hole
Peng Liu, Chao Niu, Cheng-Yong Zhang
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We studied the instability of the regularized 4D charged Einstein-Gauss-Bonnet de-Sitter black holes under charged scalar perturbations. The unstable modes satisfy the superradiant condition, but not all modes satisfying the superradiant condition are unstable. The instability occurs when the cosmological constant is small and the black hole charge is not too large. The Gauss-Bonnet coupling constant makes the unstable black hole more unstable when both the black hole charge and cosmological constant are small, and makes the stable black hole more stable when the black hole charge is large.
Charmed and ϕ meson decay constants from 2+1-flavor lattice QCD
Ying Chen, Wei-Feng Chiu, Ming Gong, Zhaofeng Liu, Yunheng Ma
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On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical pion mass, we calculate the decay constants of \begin{document}$ D_{s}^{(*)} $\end{document}, \begin{document}$ D^{(*)} $\end{document} and \begin{document}$ \phi $\end{document}. The lattice size is \begin{document}$ 48^3\times96 $\end{document}, which corresponds to a spatial extension of \begin{document}$ \sim5.5 $\end{document} fm with the lattice spacing \begin{document}$ a\approx 0.114 $\end{document} fm. For the valence light, strange and charm quarks, we use overlap fermions at several mass points close to their physical values. Our results at the physical point are \begin{document}$ f_D = 213(5) $\end{document} MeV, \begin{document}$ f_{D_s} = 249(7) $\end{document} MeV, \begin{document}$ f_{D^*} = 234(6) $\end{document} MeV, \begin{document}$ f_{D_s^*} = 274(7) $\end{document} MeV, and \begin{document}$ f_\phi = 241(9) $\end{document} MeV. The couplings of \begin{document}$ D^* $\end{document} and \begin{document}$ D_s^* $\end{document} to the tensor current (\begin{document}$ f_V^T $\end{document}) can be derived, respectively, from the ratios \begin{document}$ f_{D^*}^T/f_{D^*} = 0.91(4) $\end{document} and \begin{document}$ f_{D_s^*}^T/f_{D_s^*} = 0.92(4) $\end{document}, which are the first lattice QCD results. We also obtain the ratios \begin{document}$ f_{D^*}/f_D = 1.10(3) $\end{document} and \begin{document}$ f_{D_s^*}/f_{D_s} = 1.10(4) $\end{document}, which reflect the size of heavy quark symmetry breaking in charmed mesons. The ratios \begin{document}$ f_{D_s}/f_{D} = 1.16(3) $\end{document} and \begin{document}$ f_{D_s^*}/f_{D^*} = 1.17(3) $\end{document} can be taken as a measure of SU(3) flavor symmetry breaking.
Dibaryons: Molecular versus Compact Hexaquarks
H. Clement, T. Skorodko
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Hexaquarks constitute a natural extension of complex quark systems like also tetra- and pentaquarks do. To this end the current status of \begin{document}$d^*(2380)$\end{document} in both experiment and theory is reviewed. Recent high-precision measurements in the nucleon-nucleon channel and analyses thereof have established \begin{document}$d^*(2380)$\end{document} as an indisputable resonance in the long-sought dibaryon channel. Important features of this \begin{document}$I(J^P) = 0(3^+)$\end{document} state are its narrow width and its deep binding relative to the \begin{document}$\Delta(1232)\Delta(1232)$\end{document} threshold. Its decay branchings favor theoretical calculations predicting a compact hexaquark nature of this state. We review the current status of experimental and theoretical studies on \begin{document}$d^*(2380)$\end{document} as well as new physics aspects it may bring in the future. In addition, we review the situation at the \begin{document}$\Delta(1232) N$\end{document} and \begin{document}$N^*(1440)N$\end{document} thresholds, where evidence for a number of resonances of presumably molecular nature have been found --- similar to the situation in charmed and beauty sectors. Finally we briefly discuss the situation of dibaryon searches in the flavored quark sectors.
Systematic study of α decay half-lives within the Generalized Liquid Drop Model with various versions of proximity energies
Jun-Gang Deng, Hong-Fei Zhang
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It is universally acknowledged that the Generalized Liquid Drop Model (GLDM) has two advantages that over other α decay theoretical models: introducing the quasimolecular shape mechanism and proximity energy. In the past few decades, the original proximity energy has been improved by numerous works. In the present work, the different improvements of proximity energy are examined when they are applied to GLDM for enhancing the calculation accuracy and prediction ability of α decay half-lives for known and unsynthesized superheavy nuclei. The calculations of α half-lives have systematic improvements in reproducing experimental data after choosing a more suitable proximity energy applied to GLDM. Encouraged by this, the α decay half-lives of even-even superheavy nuclei with Z=112-122 are predicted by the GLDM with a more suitable proximity energy. The predictions are consistent with calculations by the improved Royer formula and the universal decay law. In addition, the features of predicted α decay half-lives imply that the next double magic nucleus after 208Pb is 298Fl.
Analyses of multi-pion Bose-Einstein correlations for granular sources with coherent pion-emission droplets
Ghulam Bary, Wei-Ning Zhang, Peng Ru, Jing Yang
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The ALICE Collaboration measure the three- and four-pion Bose-Einstein correlations (BECs) in Pb-Pb collisions at the Large Hadron Collider (LHC). It is speculated that the significant suppressions of multi-pion BECs are due to a considerable degree of coherent pion emission in the collisions. In this paper, we study the multi-pion BEC functions in a granular source model with coherent pion-emission droplets. We find that the intercepts of multi-pion correlation functions at the relative momenta near zero are sensitive to droplet number in the granular source. They decrease with decreasing droplet number. The three-pion correlation functions for the evolving granular sources with momentum-dependent partially coherent pion-emission droplets are in basic agreement with the experimental data in Pb-Pb collisions at \begin{document}$ \sqrt{s_{NN}}=2.76$\end{document} TeV at the LHC. However, the model results of four-pion correlation function are inconsistent with the experimental data. The investigations of the normalized multi-pion correlation functions of the granular sources indicate that there is an interesting enhancement of the normalized four-pion correlation function in moderate relative-momentum region.
General neutrino mass spectrum and mixing properties in seesaw mechanisms
Wojciech Flieger, Janusz Gluza
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Neutrinos stand out among elementary particles through their unusually small masses. Various seesaw mechanisms attempt to explain this fact. In this work applying insights from matrix theory we are in a position to treat variants of seesaw mechanisms in a general manner. Specifically, using Weyl's inequalities we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos. We find an estimate on the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos shifted at most by the maximal strength of the coupling to the light neutrino sector. We provide analytical conditions allowing to prescribe that precisely two out of five neutrinos are heavy. For higher-dimensional cases the inverse eigenvalue methods are used. In particular, for the CP invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones, i.e. the respective mass submatrix is positive definite, then large masses are provided by matrices with large elements accumulated on the diagonal. Finally, the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis. This general observation concerning neutrino mixing together with results on the mass spectrum properties opens directions for further neutrino physics studies using matrix analysis.
The instability of AdS black holes with lattices
Yi Ling, Meng-He Wu
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The Anti-de Sitter (AdS) black hole with lattice structure plays an essential role in the study of the optical conductivity in holographic approach. We investigate the instability of this sort of black holes which may lead to the holographic description of charge density waves. In the presence of homogeneous axion fields, we show that the instability of AdS-Reissner-Nordström(AdS-RN) black hole is always suppressed. However, in the presence of Q-lattices, we find that the unstable region becomes the smallest in the vicinity of the critical region for metal/insulator phase transition. This novel phenomenon is reminiscent of the behavior of the holographic entanglement entropy during quantum phase transition.
The Mass of Short-Range Correlated Nucleon
Rong WANG, Xu-Rong CHEN, Tao-Feng WANG
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The nucleon properties and structure should be modified by short-range correlations (SRC) among nucleons. By analyzing SRC ratio data, we extract the mass of nucleon in the SRC pair and the expected number of pn-SRC pairs in deuterium, under the assumption that the SRC nucleon mass is universal in different nuclei. The nucleon mass of a two-nucleon SRC pair is \begin{document}$m_{\rm{SRC}}$\end{document}=852 ± 18 MeV, and the number of pn-SRC pairs in deuterium is \begin{document}$n^{\rm{d}}_{\rm{SRC}}$\end{document}=0.021 ± 0.005. The mass deficit of the strongly overlapping nucleon can be explained by the trace anomaly contribution to the mass in QCD or alternatively by the vacuum energy in the MIT bag model.
Muon Flux Measurement at China Jinping Underground Laboratory
Zi-yi Guo, Lars Bathe-Peters, Shao-min Chen, Mourad Chouaki, Wei Dou, Lei Guo, Ghulam Hussain, Jin-jing Li, Qian Liu, Guang Luo, Wen-tai Luo, Ming Qi, Wen-hui Shao, Jian Tang, Lin-yan Wan, Zhe Wang, Ben-da Xu, Tong Xu, Wei-ran Xu, Yu-zi Yang, Minfang Yeh, Lin Zhao
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China Jinping Underground Laboratory (CJPL) is ideal for studying solar-, geo-, and supernova neutrinos. A precise measurement of the cosmic-ray background would play an essential role in proceeding with the R&D research for these MeV-scale neutrino experiments. Using a 1-ton prototype detector for the Jinping Neutrino Experiment (JNE), we detected 264 high-energy muon events from a 645.2-day dataset at the first phase of CJPL (CJPL-I), reconstructed their directions, and measured the cosmic-ray muon flux to be \begin{document}$(3.53\pm0.22_{\rm{stat.}}\pm0.07_{\rm{sys.}})\times10^{-10}$\end{document} cm\begin{document}$^{-2}$\end{document}s\begin{document}$^{-1}$\end{document}. The observed angular distributions indicate the leakage of cosmic-ray muon background and agree with the simulation accounting for Jinping mountain's terrain. A survey of muon fluxes at different laboratory locations situated under mountains and below mine shaft indicated that the former is generally a factor of \begin{document}$(4\pm2)$\end{document} larger than the latter with the same vertical overburden. This study provides a convenient back-of-the-envelope estimation for muon flux of an underground experiment.
Systematic study of the Woods-Saxon potential parameters between heavy-ions
Lin GAN, Hong-Li ZHI, Hui-Bin SUN, Shi-Peng HU, Er-Tao LI, Jian ZHONG
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Experimental elastic scattering angular distributions of 11B, 12C and 16O + heavy-ions were used to study the Woods-Saxon potential parameters. The diffuseness parameters were found to have best fitted values for each system, and a linear expression of diffuseness parameters with \begin{document}$A_1^{1/3}+A_2^{1/3}$\end{document} was summarized. The correlations of potential depths and radius parameters with \begin{document}$A_1^{1/3}+A_2^{1/3}$\end{document} were revealed with the limitation of diffuseness parameter formula. As the incident energies of most analyzed reactions are below and around the Coulomb barrier, the energy dispersion relation between the real and imaginary potentials was taken into consideration to study the ratio of the imaginary and real potential well depths, and the expression of \begin{document}$W/V$\end{document} was concluded. With the limitation of volume integrals calculated with S\begin{document}$\tilde{a}$\end{document}o Paulo potential, parameterized formulas for depths and radius parameters were obtained. The deduced systematic Woods-Saxon potential parameters in present work can reproduce not only the experimental data of elastic scattering angular distributions induced by 11B, 12C and 16O, but also some elastic scattering induced by other heavy-ions.
J/Ψ-J/Ψ scattering cross sections of Quadratic and Cornell Potentials
M. Imran Jamil, S.M. Sohail Gilani, Ahmad Wasif, Abdul Sattar Khan, Ahmad Awan
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We study the scattering of J/\begin{document}$\Psi$\end{document} - J/\begin{document}$\Psi$\end{document} mesons using quadratic and Cornell potentials in our tetraquark (\begin{document}${\rm{c\bar cc\bar c}}$\end{document}) system. The system’s wavefunction in the restricted gluonic basis is written by utilizing adiabatic approximation and Hamiltonian is used via quark potential model. Resonating group technique is used to get the integral equations which are solved to get the unknown inter-cluster dependence of the total wavefunction of our tetraquark system. T-Matrix elements are calculated from the solutions and eventually the scattering cross sections are obtained using the two potentials respectively. We compare these cross sections and find that the magnitude of scattering cross sections of quadratic potential are higher than Cornell potential.
Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data
Wenchang Xiang, Mengliang Wang, Yanbing Cai, Daicui Zhou
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We analytically solve the Sudakov suppressed Balitsky-Kovchegov evolution equation with the fixed and running coupling constants in the saturation region. The analytic solution of the S-matrix shows the \begin{document}$\exp(-{\cal{O}}(\eta^2))$\end{document} rapidity dependence of the solution with the fixed coupling constant is replaced by \begin{document}$\exp(-{\cal{O}}(\eta^{3/2}))$\end{document} dependence in the smallest dipole running coupling case rather than obeying the law found in our previous publication, in which all the solutions of the next-to-leading order evolution equations comply with \begin{document}$\exp(-{\cal{O}}(\eta))$\end{document} rapidity dependence once the QCD coupling is switched from the fixed coupling to the smallest dipole running coupling prescription. This finding indicates that the corrections of the sub-leading double logarithms in the Sudakov suppressed evolution equation are significant, which compensate part of the evolution decrease of the dipole amplitude made by running coupling effect. To test the analytic findings, we calculate the numerical solutions of the Sudakov suppressed evolution equation, the numerical results confirm the analytic outcomes. Moreover, we use the numerical solutions of the evolution equation to fit the HERA data. It shows that the Sudakov suppressed evolution equation can give good quality fit to the data.
Analysis of strong refractive effect within 11Li projectile structure
Kassem O. Behairy, M. El-Azab Farid, Awad A. Ibraheem, Ola. Ramadan, M. Anwar
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In the context of the double folding optical model, the strong refractive effect for elastic scattering of 11Li + 12C, 11Li +28Si systems at incident energy 29, 50 and 60 MeV/n has been studied. Real folded potentials are generated based on a variety of nucleon-nucleon interactions with the suggested density distribution for the halo structure of 11Li nuclei. The rearrangement term (RT) of the extended realistic density dependent CDM3Y6 effective interaction is considered. The imaginary potential was taken in traditional standard Woods-Saxon form. Satisfactory results for the calculated potentials are obtained, with a slight effect of the RT in CDM3Y6 potential. Successful reproduction with normalization factor closed to one for the observed angular distributions of the elastic scattering differential cross section has been achieved using the derived potentials. The obtained reaction cross-section is studied as a guide by extrapolating our calculations and previous results.
Band mixing of 96,98Mo isotopes
A. Jalili Majarshin, Yan-An Luo, Feng Pan, Jerry P. Draayer
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We have used the lowest weight two states to fit E2 strengths connecting the \begin{document}$0\leftrightarrow 2$\end{document} and \begin{document}$2\leftrightarrow 4$\end{document} transitions in \begin{document}$^{96,98}$\end{document}Mo. Our results confirm that the \begin{document}$2^+$\end{document} and \begin{document}$4^+$\end{document} states are maximally mixed, the \begin{document}$0^+$\end{document} states are weakly mixed in both nuclei. An appropriate Hamiltonian to represent the band mixing is found to be exactly solvable, and its eigenstates can be expressed as the basis vectors in the configuration mixing scheme and interacting boson model. The interacting boson model and coexistence mixing configuration under the solvable methods are suitable models to analyze the band mixing with high accuracy.
The implications of the axion like particle from the Fermi-LAT and H.E.S.S. observations of PG 1553+113 and PKS 2155−304
Jun-Guang Guo, Hai-Jun Li, Xiao-Jun Bi, Su-Jie Lin, Peng-Fei Yin
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We investigate the axion like particle (ALP)-photon oscillation effect in the high energy \begin{document}$\gamma$\end{document}-ray spectra of PG 1553+113 and PKS 2155−304 measured by Fermi-LAT and H.E.S.S.. The choice of extragalactic background light (EBL) model, which induces the attenuation effect in observed \begin{document}$\gamma$\end{document}-ray spectra, would affect the ALP implication. For the ordinary EBL model that prefers a null hypothesis, we set constraint on the ALP-photon coupling constant at 95% C.L. as \begin{document}$g_{a\gamma}\lesssim 5\times 10^{-11} ~{\rm{GeV}}^{-1}$\end{document} for the ALP mass \begin{document}$\sim 10$\end{document} neV. We also consider the CIBER observation of the cosmic infrared radiation, which shows an excess at the wave wavelength of \begin{document}$\sim 1~\mu$\end{document}m after the substraction of foregrounds. The high energy gamma-rays from extragalactic sources at high redshifts would suffer from a more significant attenuation effect caused by this excess. In this case, we find that the ALP-photon oscillation would improve the fit to the observed spectra of PKS 2155−304 and PG 1553+113 and find a favored parameter region at 95% C.L..
Medium modifications of girth distributions for inclusive jets and Z0+jet in relativistic heavy-ion collisions at the LHC
Jun Yan, Shi-Yong Chen, Wei Dai, Ben-Wei Zhangy, Enke Wang
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In this paper we investigate the medium modifications of girth distributions for inclusive jets and \begin{document}$Z^0$\end{document} tagged jets with small radius (\begin{document}$R=0.2$\end{document}) in Pb+Pb collisions with \begin{document}$\sqrt{s}=2.76$\end{document} TeV at the LHC. The partonic spectrum in the initial hard scattering of elementary collisions are obtained by a event generator POWHEG+PYTHIA, which matches the next-to-leading (NLO) matrix elements with parton showering, and energy loss of fast parton traversing in hot/dense QCD medium is calculated by Monte Carlo simulation within Higher-Twist formalism of jet quenching in heavy-ion collisions. We present the model calculations of event normalized girth distributions for inclusive jets in p+p and Pb+Pb collisions at \begin{document}$\sqrt{s}=2.76$\end{document} TeV, which give nice descriptions of ALICE measurements. It is shown that the girth distributions of inclusive jets in Pb+Pb are shifted to lower girth region relative to that in p+p. Thus the nuclear modification factor of girth distributions for inclusive jets is larger than unity at small girth region, while smaller than one at large girth region. This behavior results from more soft fragments inside a jet as well as the fraction alteration of gluon/quark initiated jets in heavy-ion collisions. We further predict the girth distributions for \begin{document}$Z^0$\end{document} boson tagged jets in Pb+Pb collisions at \begin{document}$\sqrt{s}=2.76$\end{document} TeV, and demonstrate that the medium modification on girth distributions for \begin{document}$Z^0$\end{document} tagged jets is less pronounced as compared to that for inclusive jets because the dominant components of \begin{document}$Z^0$\end{document} tagged jets are quark-initiated jets.
Strong cosmic censorship for a scalar field in an Einstein-Maxwell-Gauss-Bonnet-de Sitter black hole
Qingyu Gan, Peng Wang, Houwen Wu, Haitang Yang
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It has been shown that the Christodoulou version of the Strong Cosmic Censorship (SCC) conjecture can be violated for a scalar field in a near-extremal Reissner-Nordstrom-de Sitter black hole. In this paper, we investigate the effects of higher derivative corrections to the Einstein-Hilbert action on the validity of SCC, by considering a neutral massless scalar perturbation in \begin{document}$ 5 $\end{document}- and \begin{document}$ 6 $\end{document}-dimensional Einstein-Maxwell-Gauss-Bonnet-de Sitter black holes. Our numerical results exhibit that the higher derivative term plays a different role in the \begin{document}$ d = 5 $\end{document} case than it does in the \begin{document}$ d = 6 $\end{document} case. For \begin{document}$ d = 5 $\end{document}, the SCC violation region increases as the strength of the higher derivative term increases. For \begin{document}$ d = 6 $\end{document}, the SCC violation region first increases and then decreases as the higher derivative correction becomes stronger, and SCC can always be restored for a black hole with a fixed charge ratio when the higher derivative correction is strong enough. Finally, we find that the \begin{document}$ C^{2} $\end{document} version of SCC is respected in the \begin{document}$ d = 6 $\end{document} case, but can be violated in some near-extremal regime in the \begin{document}$ d = 5 $\end{document} case.
Multi-quasiparticle excitations and the impact of high-j intruder orbital in the N = 51 nucleus 93Mo
Hao Wang, Ke-Yan Ma, Yi-Heng Wu, Yi-Feng Lv, Hao-Nan Pan, Jing-Bin Lu
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The level structures of \begin{document}$^{93}$\end{document}Mo are investigated using the Large Scale Shell Model calculations. A reasonable agreement between the experimental and calculated values is obtained. The calculated results show that the lower-lying states are mainly dominated by the proton excitations from the \begin{document}$1f_{5/2}$\end{document}, \begin{document}$2p_{3/2}$\end{document} and \begin{document}$2p_{1/2}$\end{document} orbitals into the higher orbitals across the Z = 38 or Z = 40 subshell closure. For the higher-spin states, the multi-particle excitations including a \begin{document}$2d_{5/2}$\end{document} neutron across the N = 56 subshell closure into the high-j intruder \begin{document}$1h_{11/2}$\end{document} orbital are essential. Moreover, the previous unknown spin-parity assignments of the six higher excited states in \begin{document}$^{93}$\end{document}Mo are reasonably inferred from shell model calculations.
The universal function of the diffractive process in color dipole picture
Z. Jalilian, G. R. Boroun
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In this presentation, we obtain the corresponding universal function to the diffractive process and show the cross section exhibits the geometrical scaling. It is observed the diffractive theory according to the color dipole approach at small-x is a convenient framework that reveals the color transparency and the saturation phenomena. Also we calculate the contribution of heavy quark productions in the diffractive cross section for high energy that is determined by the small size dipole configuration. The ratio of the diffractive cross section to the total cross section in the electron-proton collision is the other important quantity that is computed in this work.
The complete study on polarization of $ {\Upsilon }$(nS) hadroproduction at QCD next-to-leading order
Yu Feng, Bin Gong, Chao-Hsi Chang, Jian-Xiong Wang
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Applying the nonrelativistic quantum chromodynamics factorization formalism to the \begin{document}$ \Upsilon(1S,2S,3S) $\end{document} hadroproduction, a complete analysis on the polarization parameters \begin{document}$ \lambda_{\theta} $\end{document}, \begin{document}$ \lambda_{\theta\phi} $\end{document}, \begin{document}$ \lambda_{\phi} $\end{document} for the production are presented at QCD next-to-leading order. With the long-distance matrix elements extracted from experimental data for the production rate and polarization parameter \begin{document}$ \lambda_{\theta} $\end{document} of \begin{document}$ \Upsilon $\end{document} hadroproduction, our results provide a good description for the measured parameters \begin{document}$ \lambda_{\theta\phi} $\end{document} and \begin{document}$ \lambda_{\phi} $\end{document} in both the helicity and the Collins-Soper frames. In our calculations the frame invariant parameter \begin{document}$ \tilde{\lambda} $\end{document} is consistent in the two frames. Finally, it is pointed out that there are discrepancies for \begin{document}$ \tilde{\lambda} $\end{document} between available experimental data and corresponding theoretical predictions.
Improved empirical formula for α particle preformation factor
Yan He, Xuan Yu, Hongfei Zhang
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In this contribution, the \begin{document}$\alpha$\end{document} preformation factors of 606 nuclei are extracted within the framework of generalized liquid drop model (GLDM). Through the systematically analysis of the \begin{document}$\alpha$\end{document} preformation factors of even-even Po-U isotopes, we found there is a significant weakening of influence of \begin{document}$N=126$\end{document} shell closure in uraninum, which is consistent with the result of a recent experiment [J. Khuyagbaatar et al., Phys. Rev. Lett. 115.242502 (2015)], implying that \begin{document}$N=126$\end{document} may be not the magic number for U isotopes. Furthermore, we propose an improved formula with only 7 parameters to calculate \begin{document}$\alpha$\end{document} preformation factors suitable for all types of \begin{document}$\alpha$\end{document}-decay, which has fewer parameters than the original formula proposed by Zhang et al. [H. F. Zhang et al., Phys. Rev. C 80.057301 (2009)] with high precision. The standard deviation of the \begin{document}$\alpha$\end{document} preformation factors calculated by our formula with extracted values for all 606 nuclei is 0.365 with a factor of 2.3, indicating that our improved formula can accurately reproduce the \begin{document}$\alpha$\end{document} preformation factors. Encouraged by this, the \begin{document}$\alpha$\end{document}-decay half-lives of actinide elements are predicted, which could be useful in future experiments. Noticeably, the predicted \begin{document}$\alpha$\end{document}-decay half-lives of two new isotopes \begin{document}$^{220}$\end{document}Np [Z.Y. Zhang, et al., Phys. Rev. Lett. 122. 192503 (2019)] and \begin{document}$^{219}$\end{document}Np [H. B. Yang et al., Phys. Lett. B 777, 212 (2018)] are in good agreement with the experimental \begin{document}$\alpha$\end{document}-decay half-lives.
Theory for quarkonium: from NRQCD factorization to soft gluon factorization
An-Ping Chen, Yan-Qing Ma
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We demonstrate that the recently proposed soft gluon factorization (SGF) is equivalent to the nonrelativistic QCD (NRQCD) factorization for heavy quarkonium production or decay, which means that for any given process these two factorization theories are either both valid or both violated. We use two methods to achieve this conclusion. In the first method, we apply the two factorization theories to the physical process \begin{document}$J/\psi \to e^+e^-$\end{document}. Our explicit calculation shows that both SGF and NRQCD can correctly reproduce low energy physics of full QCD, and thus the two factorizations are equivalent. In the second method, by using equations of motion we successfully deduce SGF from NRQCD effective field theory. By identifying SGF with NRQCD factorization, we establish relations between the two factorization theories and prove the generalized Gremm-Kapustin relations as a by product. Comparing with the NRQCD factorization, the advantage of SGF is that it resums the series of relativistic corrections originated from kinematic effects to all powers, which gives rise to a better convergence in relativistic expansion.
The eccentricity enhancement effect of intermediate-mass-ratio-inspirals: dark matter and black hole mass
Meirong Tang, Zhaoyi Xu, Jiancheng Wang
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It was found that the dark matter (DM) in the intermediate-mass-ratio-inspiral (IMRI) system has a significant enhancement effect on the orbital eccentricity of the stellar massive compact object, such as a black hole (BH), which may be tested by space-based gravitational wave (GW) detectors including LISA, Taiji and Tianqin in future observations [1]. In this paper, we will study the enhancement effect of the eccentricity for an IMRI under different DM density profiles and center BH masses. Our results are as follows: (1) in terms of the general DM spike distribution, the enhancement of the eccentricity is basically consistent with the power-law profile, which indicates that it is reasonable to adopt the power-law profile; (2) in the presence of DM spike, the different masses of the center BH will affect the eccentricity, which provides a new way for us to detect the BH's mass; (3) considering the change of the eccentricity in the presence and absence of DM spike, we find that it is possible to distinguish DM models by measuring the eccentricity at the scale of about \begin{document}$ 10^{5} GM/c^{2} $\end{document}.
Lorentz Violation, Quantum Tunneling and Information Conservation
Guo-Ping Li, Ke-Jian He, Bing-Bing Chen
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In this paper, by introducing a Lorentz-invariance-violation (LIV) class of dispersion relations (DR) suppressed by the second power \begin{document}$ (E/E_{QG})^2 $\end{document}, we have investigated the effect of LIV on the Hawking radiation of the charged Dirac particle via tunneling from a Reissner-Nordström(RN) black hole. We first find the effect of LIV speeds up the black hole evaporation, leaving the induced Hawking temperature very sensitive to the changes in the energy of the radiation particle, but at the same energy level, insensitive to the changes in the charge of the radiation particle. This provides a phenomenological evidence for the LIV-DR as a candidate for describing the effect of quantum gravity. Then, when the effect of LIV is included, we find the statistical correlations with the Planck-scale corrections between the successive emissions can leak out the information through the radiation. And, it turns out that the black hole radiation as tunneling is an entropy conservation process, and no information loss occurs during the radiation, where the interpretation for the entropy of black hole is addressed. Finally, we conclude that black hole evaporation is still an unitary process in the context of quantum gravity.
Neutron star cooling and GW170817 constraint within quark-meson coupling models
Odilon Lourenço, César H. Lenzi, Mariana Dutra, Tobias Frederico, M. Bhuyan, Rodrigo Negreiros, César V. Flores, Guilherme Grams, Débora P. Menezes
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In the present work, we used five different versions of the quark-meson coupling (QMC) model to compute astrophysical quantities related to the GW170817 event and neutron star cooling process. Two of the models are based on the original bag potential structure and three versions consider a harmonic oscillator potential to confine the quarks. The bag-like models also incorporate the pasta phase used to describe the inner crust of neutron stars. Within the simple method studied in the present work, we show that the pasta phase does not play a significant role. Moreover, the QMC model that satisfies the GW170817 constraints with the lowest slope of the symmetry energy exhibits a cooling profile compatible with observational data.
Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow
Xiao Liu, Yan-Qing Ma, Wei Tao, Peng Zhang
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We extend the auxiliary-mass-flow (AMF) method originally developed for Feynman loop integration to calculate integrals involving also phase-space integration. Flow of the auxiliary mass from the boundary (\begin{document}$\infty$\end{document}) to the physical point (\begin{document}$0^+$\end{document}) is obtained by numerically solving differential equations with respective to the auxiliary mass. For problems with two or more kinematical invariants, the AMF method can be combined with traditional differential-equation method by providing systematical boundary conditions and highly nontrivial self-consistent check. The method is described in detail with a pedagogical example of \begin{document}$e^+e^-\rightarrow \gamma^* \rightarrow t\bar{t}+X$\end{document} at NNLO. We show that the AMF method can systematically and efficiently calculate integrals to high precision.
On-shell mediator dark matter models and the Xenon1T excess
Mingxuan Du, Jinhan Liang, Zuowei Liu, Van Que Tran, Yilun Xue
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We present a dark matter model to explain the excess events in the electron recoil data recently reported by the Xenon1T experiment. In our model, dark matter \begin{document}$\chi$\end{document} annihilates into a pair of on-shell particles \begin{document}$\phi$\end{document} which subsequently decay into \begin{document}$\psi \psi$\end{document} final state; \begin{document}$\psi$\end{document} interacts with electron to generate the observed excess events. Due to the mass hierarchy, the velocity of \begin{document}$\psi$\end{document} can be rather large and can have an extended distribution, which provides a good fit to the electron recoil energy spectrum. We estimated the flux of \begin{document}$\psi$\end{document} from dark matter annihilations in the galaxy and further determined the interaction cross section which is sizable but small enough to allow \begin{document}$\psi$\end{document} to penetrate the rocks to reach the underground labs.